A very long time ago, I had the good fortune to read George Gamow's excellent series of Mr. Tompkins books. That introduced me to the idea of a world where the usual physical constants (e.g. the speed of light and Planck's constant) were changed such that "paradoxical" effects became apparent in the macroworld.

My memory is hazy now, but I do recall the concepts of relativity (e.g. dilation) becoming more pronounced when the speed of light is reduced to "human-sized" speeds.

In this vein, I ask this: assuming all other physical constants being fixed, what exactly can be expected to happen if (physical constant of your choice) is increased/or decreased?

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I suppose that you realize that books such Mr. Tompkins are not physical at all. In them it is supposed that speed of light is decreased but that people are still the same old people which is inconsistent because people are made of elementary particles that would also need to obey new speed limit and so life (and probably also any composite matter) would cease to be possible. So are you asking for real physical effects (which usually imply that life becomes impossible) or unphysical magnified effects for better illustration of the phenomena (as in Mr. Tompkins)?
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MarekDec 3 '10 at 14:08

@Marek: I meant the question in a speculative spirit; that is to say, what would we be observing if we increase or decrease a certain physical constant?
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user172Dec 3 '10 at 14:11

M.: it all depends on how precise you want to be. If you want to be very precise you can't really say anything because we don't know anything about complex structures in any other universe than our own. If you don't want to be precise, you are really just asking for personification of some natural effect (like Doppler shifts, length contraction, time dilation, etc.). So please answer which question are you asking: complete implication for real physics, or just personified explanation of some individual effects?
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MarekDec 3 '10 at 16:07

As a side note, I think a much more interesting/entertaining question is "what if the physical constants were allowed to change very slowly over space-time"?
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Sklivvz♦Dec 4 '10 at 13:52

2 Answers
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See Smolin's book "The Life of the Cosmos", here and here, wherein he suggests common descent and Darwinian selection amongst multiverses for peturbed physical constants maximizing black hole formation in that universe. His most recent paper on arxiv on this topic is http://arxiv.org/abs/hep-th/0612185, where he argues that this is still a live hypothesis, which has already survived several experimental tests.

Increasing the value of $\hbar$ significantly would be pretty interesting, as matter has a wavelength proportional to it. Walking through a doorway might become a new experience as you get diffracted into a wall.

However, this is all backwards thinking. The physical constants calibrate our mathematical models of the universe, like $\lambda = h/p$, not the other way around. So it is better to say that if you got diffracted every time you walked through a doorway, you would need a large $\hbar$ to model that.

Additionally, since constants like $\hbar$ have units, their value is somewhat arbitrary anyway. Which brings us to dimensionless constants... here's a good one:

Value of dimensionful constants is not really arbitrary. This is because there exist various scales in the nature. That is, speed of light is big with respect to normal velocities we observe around us (and SI system reflects this in the concept of second and meter). It's true that these are arbitrary scales of human beings but it's precisely they what allows Gamow to talk about small speed of light. Problem is, once you redefine some constant the matter will not able to form compounds and you'll lose all scales needed to talk about the change in (dimensionful) constants anyway.
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MarekDec 3 '10 at 16:02

The existence of scales does not negate the fact that you can make dimensionful constants whatever you want. "speed of light is big with respect to normal velocities we observe around us". That's a dimensionless constant $c/v_{\rm{normal}}$. Can't I find units where c = hbar = e = G = K = ... = 1?
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PeteDec 3 '10 at 16:32

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@Pete: oh, if you meant your statements in this way then I completely agree with you. Scales are what enables us to define dimensionless constants and then it's indeed true that only those are really physical.
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MarekDec 3 '10 at 20:35

I wonder, can I really define units where all the physical constants are 1? Or do I run out of degrees of freedom at some point?
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PeteDec 3 '10 at 20:51

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@Pete, you run out way before that. It's one of the most important problems in modern physics. E.g. the standard model has a big bunch of finely tuned constants whose measured value is unexplained at the moment.
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Sklivvz♦Dec 3 '10 at 21:06